It is understood Eisenschimmel left her role as group marketing director and group director, culture in February. It is not known if she has a job to go.
A spokesman for Lloyds declined to comment.
Eisenschimmel completed her restructure of Lloyds marketing structure in 2012, creating a group setup to replace the individual brand units following Lloyds’ 2009 acquisition of HBOS.
She is also credited with making the group’s marketing spend more accountable, recently telling Marketing Week 85 per cent of its £300m marketing spend is now measured for return on investment, up from 15 per cent when she joined.
She also oversaw the launch of TSB and Lloyds Bank last year following the decoupling of Lloyds TSB.
It is not thought she will be replaced. Miguel-Ángel Rodríguez-Sola heads the digital, marketing and customer development group function, while Catherine Kehoe is managing director of retail brands and marketing across the group.
Eisenschimmel joined Lloyds as managing director of retail marketing and direct channels in 2010 from EDF Energy, where she had been chief brand officer and chief operating officer of its consumer business.